Linear Superposition as a Core Theorem of Quantum Empiricism
Clarifying the nature of the quantum state <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">|</mo><mi mathvariant="sans-serif">Ψ</mi><mo s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/4/217 |
| _version_ | 1797434152497184768 |
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| author | Yurii V. Brezhnev |
| author_facet | Yurii V. Brezhnev |
| author_sort | Yurii V. Brezhnev |
| collection | DOAJ |
| description | Clarifying the nature of the quantum state <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">|</mo><mi mathvariant="sans-serif">Ψ</mi><mo stretchy="false">⟩</mo></mrow></semantics></math></inline-formula> is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure—quantum superposition—is based on a set-theoretic creation of ensemble formations and invokes the following three principia: (<b>I</b>) quantum statics, (<b>II</b>) doctrine of the number in the physical theory, and (<b>III</b>) mathematization of matching the two observations with each other (quantum covariance). All of the constructs rest upon a formalization of the minimal experimental entity—the registered micro-event, detector click. This is sufficient for producing the ℂ-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the spatio-temporal concepts. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice. |
| first_indexed | 2024-03-09T10:28:06Z |
| format | Article |
| id | doaj.art-5c67f80188154d268d3135379280ac5f |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T10:28:06Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-5c67f80188154d268d3135379280ac5f2023-12-01T21:29:56ZengMDPI AGUniverse2218-19972022-03-018421710.3390/universe8040217Linear Superposition as a Core Theorem of Quantum EmpiricismYurii V. Brezhnev0Department of Quantum Field Theory, Tomsk State University, 634050 Tomsk, RussiaClarifying the nature of the quantum state <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">|</mo><mi mathvariant="sans-serif">Ψ</mi><mo stretchy="false">⟩</mo></mrow></semantics></math></inline-formula> is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure—quantum superposition—is based on a set-theoretic creation of ensemble formations and invokes the following three principia: (<b>I</b>) quantum statics, (<b>II</b>) doctrine of the number in the physical theory, and (<b>III</b>) mathematization of matching the two observations with each other (quantum covariance). All of the constructs rest upon a formalization of the minimal experimental entity—the registered micro-event, detector click. This is sufficient for producing the ℂ-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the spatio-temporal concepts. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice.https://www.mdpi.com/2218-1997/8/4/217quantum foundationsnon-axiomaticitydetector clicksensemblessuperposition principlearithmetic |
| spellingShingle | Yurii V. Brezhnev Linear Superposition as a Core Theorem of Quantum Empiricism Universe quantum foundations non-axiomaticity detector clicks ensembles superposition principle arithmetic |
| title | Linear Superposition as a Core Theorem of Quantum Empiricism |
| title_full | Linear Superposition as a Core Theorem of Quantum Empiricism |
| title_fullStr | Linear Superposition as a Core Theorem of Quantum Empiricism |
| title_full_unstemmed | Linear Superposition as a Core Theorem of Quantum Empiricism |
| title_short | Linear Superposition as a Core Theorem of Quantum Empiricism |
| title_sort | linear superposition as a core theorem of quantum empiricism |
| topic | quantum foundations non-axiomaticity detector clicks ensembles superposition principle arithmetic |
| url | https://www.mdpi.com/2218-1997/8/4/217 |
| work_keys_str_mv | AT yuriivbrezhnev linearsuperpositionasacoretheoremofquantumempiricism |